Physical layer security (PLS) technologies are expected to play an important role in the next-generation wireless networks, by providing secure communication to protect critical and sensitive information from illegitimate devices. In this paper, we propose a novel secure communication scheme where the legitimate receiver use full-duplex (FD) technology to transmit jamming signals with the assistance of simultaneous transmitting and reflecting reconfigurable intelligent surface (STARRIS) which can operate under the energy splitting (ES) model and the mode switching (MS) model, to interfere with the undesired reception by the eavesdropper. We aim to maximize the secrecy capacity by jointly optimizing the FD beamforming vectors, amplitudes and phase shift coefficients for the ESRIS, and mode selection and phase shift coefficients for the MS-RIS. With above optimization, the proposed scheme can concentrate the jamming signals on the eavesdropper while simultaneously eliminating the self-interference (SI) in the desired receiver. To tackle the coupling effect of multiple variables, we propose an alternating optimization algorithm to solve the problem iteratively. Furthermore, we handle the non-convexity of the problem by the the successive convex approximation (SCA) scheme for the beamforming optimizations, amplitudes and phase shifts optimizations for the ES-RIS, as well as the phase shifts optimizations for the MS-RIS. In addition, we adopt a semi-definite relaxation (SDR) and Gaussian randomization process to overcome the difficulty introduced by the binary nature of mode optimization of the MS-RIS. Simulation results validate the performance of our proposed schemes as well as the efficacy of adapting both two types of STAR-RISs in enhancing secure communications when compared to the traditional selfinterference cancellation technology.